Superconductivity, Charge-Density-Waves, and Bipolarons in the Holstein model

TL;DR

This study uses quantum Monte Carlo simulations to explore how electron-phonon interactions influence superconductivity, charge-density-waves, and polarons in the two-dimensional Holstein model across various parameters.

Contribution

It provides a comprehensive phase diagram analysis of the Holstein model, detailing the conditions favoring superconductivity, CDW, and polaron formation, and identifies the optimal parameters for superconductivity.

Findings

Superconductivity peaks at intermediate e-ph coupling and electron density.

Superconducting correlations grow with increasing phonon frequency.

Maximum superconductivity occurs at high phonon frequencies, akin to the attractive Hubbard model.

Abstract

The electron-phonon (e-ph) interaction remains of great interest in condensed matter physics and plays a vital role in realizing superconductors, charge-density-waves (CDW), and polarons. We study the two-dimensional Holstein model for e-ph coupling using determinant quantum Monte Carlo across a wide range of its phase diagram as a function of temperature, electron density, dimensionless e-ph coupling strength, and the adiabatic ratio of the phonon frequency to the Fermi energy. We describe the behavior of the CDW correlations, the competition between superconducting and CDW orders and polaron formation, the optimal conditions for superconductivity, and the transition from the weak-coupling regime to the strong-coupling regime. Superconductivity is optimized at intermediate e-ph coupling strength and intermediate electron density, and the superconducting correlations increase monotonically with phonon frequency. The global maximum for superconductivity in the Holstein model occurs at large phonon frequency, the limit where an attractive Hubbard model effectively describes the physics.